- #1

kreil

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## Homework Statement

Consider a damped harmonic oscillator. After four cycles the amplitude of the oscillator has dropped to 1/e of its initial value. Find the ratio of the frequency of the damped oscillator to its natural frequency.

## Homework Equations

[tex]T=\frac{ 2\pi}{w_1}[/tex]

[tex] w_1^2=w_0^2- {\Beta}^2[/tex]

## The Attempt at a Solution

I know the answer is [tex]\frac{w_1}{w_0}=\frac{8 {\pi}}{\sqrt{64 {\pi}^2+1}}[/tex]

However, I think I am missing an equation here because using only the two above i cannot obtain this answer. If someone could point me in the right direction I would appreciate it!

Josh

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